Wireless communication systems transfer data from a transmitter (TX) of one station to a receiver (RX) of another station. In some applications, one of the stations can be ground based (i.e., stationary) while the other station is carried by a flying object (e.g., a satellite in Earth's orbit or an airplane). In some applications, multiple stations (TX or RX) can be ground based and in communication with one or more flying objects (RX or TX). Such systems are sometimes used for Internet connections, especially if the land-based network is underdeveloped. A relative distance between the TX and RX changes in real time, depending on the direction and magnitude of the velocity of the flying object. As a result, the Doppler shift distorts the signal transmitted/received between the TX and RX. The Doppler frequency shift can be estimated as:fD=ft−fr,where ft represents frequency of the signal at TX, and fr represents frequency of the signal at RX. The Doppler frequency shift can be calculated as:
            f      D        =                  f        c            ⁢                        (                                                    V                →                            t                        -                                          V                →                            r                                )                ·                  n          →                      ,where {right arrow over (V)}t and {right arrow over (V)}r represent velocities of TX and RX, respectively, {right arrow over (n)} represents unity vector in the line of TX and RX, and “c” represents the speed of light.
In practice, if an airplane TX transmits a wireless signal while traveling away from the ground station, the frequency of the signal sensed by the ground station RX is lower than the frequency of the wireless signal originally transmitted by the airplane's TX. Conversely, if, for example, the airplane receives the wireless signal while travelling toward the ground station, the frequency of the signal sensed by the airplane's RX is higher than the frequency of the wireless signal originally transmitted from the ground station's TX. This mismatch in the TX/RX frequencies of the wireless signals can result in an increased bit error ratio (BER) of the digital signal (i.e., number of the error bits divided by the total number of bits in the signal) reduced from the received wireless signal at the RX, which reduces the effective bandwidth of the wireless signal.
Several conventional methods can counteract the mismatch between the TX and RX frequencies caused by the Doppler shift. For example, when the trajectory of the flying object is known a-priori (e.g., a commercial airplane on a scheduled route), the Doppler shift at the ground station can be calculated. Based on this predetermined Doppler shift, the wireless signal at, for example, airplane TX, can be predistorted through analogue circuitry such that the frequency shift of the wireless signal received by the ground station RX is eliminated or reduced. In other conventional systems, the a-priori known Doppler shift can be fed to appropriate electronic circuitry at the RX to correct the frequency of the signal received by the RX. The electronic circuitry required for the correction/predistortion can be either stored at the ground station or carried by the relatively large flying object (e.g., the satellite or airplane). With some other conventional systems, the flying object transmits a reference signal at known frequency in addition to the data-carrying wireless signal. The difference between the frequency of the reference signal as received by the RX and the a-priori known value of the emitted reference signal corresponds to the Doppler frequency shift. Since the wireless signal received by the RX is also subjected to the same Doppler shift, the wireless signal can be corrected using, for example, suitable electronic circuitry.
In some applications, however, the trajectory of the flying object is not known a-priori and/or the reference signals may not be practical because the bandwidth required for the reference signal reduces the bandwidth available for the wireless data transmission. Accordingly, it would be advantageous to provide a robust correction for wireless signal Doppler shift that does not depend on the a-priori knowledge of the trajectory of the flying object or on the reference signals.